numerical models for fluid-grains interactions: opportunities and limitations

In the framework of a multi-scale approach, we develop numerical models for suspension flows. At the micro scale level, we perform particle-resolved numerical simulations using a Distributed Lagrange Multiplier/Fictitious Domain approach. At the meso scale level, we use a two-way Euler/Lagrange approach with a Gaussian filtering kernel to model fluid-solid momentum transfer. At both the micro and meso scale levels, particles are individually tracked in a Lagrangian way and all inter-particle collisions are computed by a Discrete Element/Soft-sphere method. The previous numerical models have been extended to handle particles of arbitrary shape (non-spherical, angular and even non-convex) as well as to treat heat and mass transfer. All simulation tools are fully-MPI parallel with standard domain decomposition and run on supercomputers with a satisfactory scalability on up to a few thousands of cores. The main asset of multi scale analysis is the ability to extend our comprehension of the dynamics of suspension flows based on the knowledge acquired from the high-fidelity micro scale simulations and to use that knowledge to improve the meso scale model. We illustrate how we can benefit from this strategy for a fluidized bed, where we introduce a stochastic drag force model derived from micro-scale simulations to recover the proper level of particle fluctuations. Conversely, we discuss the limitations of such modelling tools such as their limited ability to capture lubrication forces and boundary layers in highly inertial flows. We suggest ways to overcome these limitations in order to enhance further the capabilities of the numerical models.